Associativity Regrouping Legality Checker
Classical pure Boolean associate identity witness for AND/OR; not short-circuit side-effect equivalence or arbitrary programming operator.
Description
Associativity Regrouping Legality Checker: return identity holds.
Associativity changes the grouping of three operands without changing their order. Boolean AND and OR satisfy this identity.
This tool returns identity holds. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Apply the selected AND or OR operation to both groupings of the supplied three booleans, then compare the results.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| operator | Operator. | Exact value: "AND", "OR" |
| a | A. | true or false |
| b | B. | true or false |
| c | C. | true or false |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.identityHolds | Identity holds flag under the exact conditions described above. |
{
"input": {
"operator": "AND",
"a": true,
"b": false,
"c": true
},
"output": {
"result": {
"identityHolds": true
}
}
}Limitations and assumptions
- The tool evaluates the declared Boolean operation; it does not justify regrouping unrelated operators.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
References
Similar or alternative tools
- a proposition classifier
Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative.
- absorption law simplifier
Absorption removes a nested combination that adds no new truth condition to its repeated leading atom.